Small prismated tesseractic tetracomb

Small prismated tesseractic tetracomb
Rank5
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymSpittit
Coxeter diagramx4o3o3x4o ()
Elements
Tera6N tesseracts, 4N cuboctahedral prisms, N rectified tesseracts, N small disprismatotesseractihexadecachora
Cells16N tetrahedra, 32N triangular prisms, 4N+24N+24N cubes, 8N cuboctahedra
Faces64N triangles, 24N+24N+96N squares
Edges48N+96N
Vertices32N
Vertex figureTriangular antifastegium, edge lengths 1 (base edges of triangular prism) and 2 (all other edges)
Related polytopes
ArmySpittit
RegimentSpittit
ConjugateQuasiprismated tesseractic tetracomb
Abstract & topological properties
OrientableYes
Properties
SymmetryR5
ConvexYes
NatureTame

The small prismated tesseractic tetracomb or spittit, also called the runcinated tesseractic tetracomb is a convex uniform tetracomb. 1 rectified tesseract, 2 small disprismatotesseractihexadecachora, 3 tesseracts, and 3 cuboctahedral prisms join at each vertex of this tessellation. As the name suggests, it is the runcination of the tesseractic tetracomb.

Vertex coordinates

The vertices of a small prismated tesseractic tetracomb of edge length 1 are given by all permutations of:

• ${\displaystyle \left(\pm {\frac {1}{2}}+(1+{\sqrt {2}})i,\,\pm {\frac {1}{2}}+(1+{\sqrt {2}})j,\,\pm {\frac {1}{2}}+(1+{\sqrt {2}})k,\,\pm {\frac {1+{\sqrt {2}}}{2}}+(1+{\sqrt {2}})l\right)}$,

where i , j , k , and l  range over the integers.

Representations

A small prismated tesseractic tetracomb has the following Coxeter diagrams:

• x4o3o3x4o () (full symmetry)
• x3o3o4x *b3x () (half symmetry)